Please note that a small amount of random noise has been added to school location coordinates in order to avoid overplotting schools that share a campus
# A tibble: 2 x 7
Phase term estimate std.error statistic p.value p.adjusted
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Primary (Intercept) 82.9 6.04 13.7 4.34e-40 3.47e-39
2 Primary Pupil_Numbers 3.20 0.0247 130. 0. 0. The regression shows that for the primary phase in Welsh schools, each individual student increases the Individual Schools Budget by £3,200. The p value returns a strong statistical significance (p adjusted = 0). Essentially, in 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is extremely low, at a value of 0.0247. This means that on average, the model will be incorrect by £25 plus or minus the median value.
Note that the nursery phase returned a non-significant p value and therefore was not analysed. This is likely due to the small number of nursery schools within Wales.
# A tibble: 2 x 7
Phase term estimate std.error statistic p.value p.adjusted
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Secondary (Intercept) 434. 66.2 6.57 4.51e- 10 2.25e- 9
2 Secondary Pupil_Numbers 4.15 0.0701 59.3 1.53e-127 1.38e-126The regression shows that for the secondary phase in Welsh schools, each individual student increases the Individual Schools Budget by £4,150. The p value returns a strong statistical significance (p adjusted = 1.38e-126). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is extremely low for this phase, at a value of 0.0701. This means that on average, the model will be incorrect by £70 plus or minus the median value.
# A tibble: 2 x 7
Phase term estimate std.error statistic p.value p.adjusted
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Middle (Intercept) 168. 196. 0.855 4.04e- 1 6.01e- 1
2 Middle Pupil_Numbers 4.39 0.224 19.6 4.22e-13 2.53e-12The regression shows that for the middle phase in Welsh schools, each individual student increases the Individual Schools Budget by £4,390. The p value returns a strong statistical significance (p adjusted = 2.53e-12). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers. The standard error is very low, at a value of 0.24. This means that on average, the model will be incorrect by £224 plus or minus the median value.
# A tibble: 2 x 7
Phase term estimate std.error statistic p.value p.adjusted
<fct> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 Special (Intercept) 228. 218. 1.05 3.01e- 1 6.01e- 1
2 Special Pupil_Numbers 18.3 1.63 11.2 9.48e-14 6.63e-13The regression shows that for the special phase in Welsh schools, each individual student increases the Individual Schools Budget by £18,300. The p value returns a strong statistical significance (p adjusted = 6.63e-13). In 99.9% of cases, an increase in ISB is explained by an increase in pupil numbers.
However, the standard error is relatively larger than the other phases in this report, at a value of 1.63. This means that on average, the model will be incorrect by £1,630 plus or minus the median value. This increase in standard error is symptomatic of having a relatively small sample size in relation to the correlation coefficient and therefore would advise caution in drawing conclusions from this dataset.